1. Perfect Square Roots & Approximating Non-Perfect Square Roots
8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). 
8th Grade Math – Miss. Audia

2. Square Roots - A value that, when multiplied by itself, gives the number (ex. √36=±6). Perfect Squares - A number made by squaring an integer. Integer – A number that is not a fraction. Remember The answer to all square roots can be either positive or negative. We write this by placing the ± sign in front of the number.

3. What are the following square roots?

4. √1

5. √4

6. √9

7. √16

8. √25

9. √36

10. √49

11. √64

12. √81

13. √100

14. √121

15. √144

16. √169

17. √196

18. √225

19. Let’s Mix It Up

20. √36

21. √121

22. √1

23. √9

24. √64

25. √225

26. √4

27. √25

28. √196

29. √169

30. √16

31. √49

32. √100

33. √81

34. √144

35. All Square Roots of Perfect Squares are Rational Numbers!
Rational Numbers – Numbers that can be written as a ratio or fraction. These numbers can also be written as terminating decimals or repeating decimals.
Terminating Decimals – A decimal that does not go on forever (ex. O.25).
Repeating Decimals – A decimal that has numbers that repeat forever
(ex. 0.3, 0.372)

36. The Square Roots of Non-Perfect Squares are Irrational Numbers
The Square Roots of Non-Perfect Squares are Irrational Numbers. Irrational Numbers – Numbers that are not Rational. They cannot be written as ratios or fractions. They are decimals which never end or repeat. Examples: π, √2, √83

37. The square roots of perfect squares are rational numbers and can be place on a number line.√1 √4 √9
√16
√25
√36
The square roots of non-perfect squares are irrational numbers. We cannot pinpoint their location on a number line, however we can approximate it.

38. Approximate where the following square roots would be on the number line: √2, √7, √31√1 √4 √9
√16
√25
√36

39. Approximate where the following square roots would be on the number line: √2, √7, √31√1 √2 √4 √7 √9
√16
√25
√31
√36